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  • Cited by 3
Cambridge University Press
Online publication date:
January 2020
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Book description

Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.


‘McMullen (emer., University College London) begins the text with a rapid, cogent review of relevant topics in linear algebra and group theory and proceeds to a thorough discussion of the properties and structures of geometric and abstract regular polytopes. The majority of the text details the classification and properties of geometric regular polytopes … This is a careful, comprehensive survey of the topic and will likely become a classic reference.’

C. A. Gorini Source: Choice

‘This book, along with his previous book … is well-written and indispensable for every researcher or every student who wants to pursue research in this area.’

Uma Kant Sahoo Source: Encyclopedia of Mathematics and its Applications

‘The book is without a doubt a modern bible on the current state of polytopes. It is no exaggeration to say that 'all of it' can be found in this book …’

Peter McMullen Source: Nieuw Archief voor Wiskunde

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